Question
Sat January 28, 2012 By:

What is Harmonic Progression ? What is Harmonic Series ? Is there any formula to find sum to 'n' terms in a harmonic progression ?

Expert Reply
Sun January 29, 2012

In mathematics, a harmonic progression is a progression formed by taking the reciprocals of an arithmetic progression. In other words, it is a sequence of the form

where ?1/d is not a natural number.

the harmonic series is the divergent infinite series:

Every term of the series after the first is the harmonic mean of the neighboring terms.

There isn't a good closed form expression. As a special case, one has the Harmonic numbers



There isn't even a good closed form expression for this particular sum, although there is a good approximation



where is the Euler-Mascheroni constant. Similar approximations can be given for more general sums of harmonic progressions.
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